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1.
August Florian 《Monatshefte für Mathematik》2007,40(4):39-43
The paper [3] contains an upper bound to the weighted density of a packing of circles on the unit sphere with radii from a
given finite set. This bound is attained by many packings and has applications to problems of solidity. In the present note
it is shown that a certain condition imposed on the set of admissible radii can be removed by modifying the original proof
of the theorem. 相似文献
2.
Rafael López 《Monatshefte für Mathematik》2008,154(4):289-302
In this paper we study surfaces in Euclidean 3-space foliated by pieces of circles that satisfy a Weingarten condition of
type aH + bK = c, where a,b and c are constant, and H and K denote the mean curvature and the Gauss curvature respectively. We prove that such a surface must be a surface of revolution,
one of the Riemann minimal examples, or a generalized cone.
Authors’ address: Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain 相似文献
3.
August Florian 《Monatshefte für Mathematik》2001,133(2):111-129
In this paper we provide an upper bound to the density of a packing of circles on the sphere, with radii selected from a
given finite set. This bound is precise, e.g. for the system of incircles of Archimedean tilings (4, 4, n) with n ? 6. A generalisation to the weighted density of packing is applied to problems of solidity of a packing of circles. The
simple concept of solidity was introduced by L. Fejes Toóth [6]. In particular, it is proved that the incircles of the faces of the Archimedean tilings
(4,6,6), (4,6,8) and (4, 6, 10) form solid packings.
(Received 21 August 2000; in revised form 21 March 2001) 相似文献
4.
Thomas C. Hales 《Combinatorica》1993,13(2):181-197
This paper shows how the density of sphere packings of spheres of equal radius may be studied using the Delaunay decomposition. Using this decomposition, a local notion of density for sphere packings in 3 is defined. Conjecturally this approach should yield a bound of 0.740873... on sphere packings in 3, and a small perturbation of this approach should yield the bound of
. The face-centered-cubic and hexagonal-close-packings provide local maxima (in a strong sense defined below) to the function which associates to every saturated sphere packing in 3 its density. The local measure of density coincides with the actual density for the face-centered cubic and hexagonal-close-packings. 相似文献
5.
Given a finite subset
of an additive group
such as
or
, we are interested in efficient covering of
by translates of
, and efficient packing of translates of
in
. A set
provides a covering if the translates
with
cover
(i.e., their union is
), and the covering will be efficient if
has small density in
. On the other hand, a set
will provide a packing if the translated sets
with
are mutually disjoint, and the packing is efficient if
has large density.
In the present part (I) we will derive some facts on these concepts when
, and give estimates for the minimal covering densities and maximal packing densities of finite sets
. In part (II) we will again deal with
, and study the behaviour of such densities under linear transformations. In part (III) we will turn to
.
Authors’ address: Department of Mathematics, University of Colorado at Boulder, Campus Box 395, Boulder, Colorado 80309-0395,
USA
The first author was partially supported by NSF DMS 0074531. 相似文献
6.
We consider finite lattice ball packings with respect to parametric density and show that densest packings are attained in critical lattices if the number of translates and the density parameter are sufficiently large. A corresponding result is not valid for general centrally symmetric convex bodies.The second author was partially supported by a DAAD Postdoc fellowship and the hospitality of Peking University during his work. 相似文献
7.
Á. G. Horváth 《Monatshefte für Mathematik》2007,150(3):211-216
This paper presents a result concerning the connection between the parallel projection P
v,H
of a parallelotope P along the direction v (into a transversal hyperplane H) and the extension P + S(v), meaning the Minkowski sum of P and the segment S(v) = {λv | −1 ≤ λ ≤ 1}. A sublattice L
v
of the lattice of translations of P associated to the direction v is defined. It is proved that the extension P + S(v) is a parallelotope if and only if the parallel projection P
v,H
is a parallelotope with respect to the lattice of translations L
v,H
, which is the projection of the lattice L
v
along the direction v into the hyperplane H. 相似文献
8.
Fabio A. C. C. Chalub Peter A. Markowich Benoît Perthame Christian Schmeiser 《Monatshefte für Mathematik》2004,142(1-2):123-141
Kinetic models for chemotaxis, nonlinearly coupled to a Poisson equation for the chemo-attractant density, are considered. Under suitable assumptions on the turning kernel (including models introduced by Othmer, Dunbar and Alt), convergence in the macroscopic limit to a drift-diffusion model is proven. The drift-diffusion models derived in this way include the classical Keller-Segel model. Furthermore, sufficient conditions for kinetic models are given such that finite-time-blow-up does not occur. Examples are given satisfying these conditions, whereas the macroscopic limit problem is known to exhibit finite-time-blow-up. The main analytical tools are entropy techniques for the macroscopic limit as well as results from potential theory for the control of the chemo-attractant density.Present address: Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal 相似文献
9.
Let be a non-negative number not greater than 1. Consider an arrangement
of (not necessarily congruent) spheres with positive homogenity in the n-dimensional Euclidean space, i.e., in which the infimum of the radii of the spheres divided by the supremum of the radii of the spheres is a positive number. With each sphere S of
associate a concentric sphere of radius times the radius of S. We call this sphere the -kernel of S. The arrangement
is said to be a Minkowski arrangement of order if no sphere of
overlaps the -kernel of another sphere. The problem is to find the greatest possible density
of n-dimensional Minkowski sphere arrangements of order . In this paper we give upper bounds on
for
. 相似文献
10.
Filippo Tolli 《Monatshefte für Mathematik》2001,133(2):163-173
We present a local limit theorem for a measure on the special linear group with entries in a local field.
(Received 20 March 2000; in revised form 8 September 2000) 相似文献
11.
12.
We treat n-dimensional compact minimal submanifolds of complex projective space when the maximal holomorphic tangent subspace is (n − 1)-dimensional and we give a sufficient condition for such submanifolds to be tubes over totally geodesic complex subspaces.
Authors’ addresses: Mirjana Djorić, Faculty of Mathematics, University of Belgrade, Studentski trg 16, pb. 550, 11000 Belgrade,
Serbia; Masafumi Okumura, 5-25-25 Minami Ikuta, Tama-ku, Kawasaki, Japan 相似文献
13.
The aim of this paper is to classify (locally) all locally homogeneous affine connections with arbitrary torsion on two-dimensional
manifolds. Herewith, we generalize the result given by B. Opozda for torsion-less case in [(2004) Classification of locally
homogeneous connections on 2-dimensional manifolds. Diff Geom Appl 21: 173–198].
Authors’ addresses: Teresa Arias-Marco, Department of Geometry and Topology, University of Valencia, Vicente Andrés Estellés
1, 46100 Burjassot, Valencia, Spain; Oldřich Kowalski, Faculty of Mathematics and Physics of the Charles University, Sokolovská
83, 18600 Praha 8, Czech Republic 相似文献
14.
For a given convex body K in
with C
2 boundary, let P
c
n
be the circumscribed polytope of minimal volume with at most n edges, and let P
i
n
be the inscribed polytope of maximal volume with at most n edges. Besides presenting an asymptotic formula for the volume difference as n tends to infinity in both cases, we prove that the typical faces of P
c
n
and P
i
n
are asymptotically regular triangles and squares, respectively, in a suitable sense.
Supported by OTKA grants 043520 and 049301, and by the EU Marie Curie grants Discconvgeo, Budalggeo and PHD.
Authors’ addresses: Károly J. B?r?czky, Alfréd Rényi Institute of Mathematics, P.O. Box 127, Budapest H–1364, Hungary, and
Department of Geometry, Roland E?tv?s University, Pázmány Péter sétány 1/C, Budapest 1117, Hungary; Salvador S. Gomis, Department
of Mathematical Analysis, University of Alicante, 03080 Alicante, Spain; Péter Tick, Gyűrű utca 24, Budapest H–1039, Hungary 相似文献
15.
O. Goubet 《Monatshefte für Mathematik》2007,151(1):39-44
We consider the so-called Gross-Pitaevskii equations supplemented with non-standard boundary conditions. We prove two mathematical
results concerned with the initial value problem for these equations in Zhidkov spaces. 相似文献
16.
Rolf Schneider 《Monatshefte für Mathematik》2007,150(3):241-247
If two convex bodies have the property that their orthogonal projections on any hyperplane have the same mean width and the
same Steiner point, then the bodies are identical. This result is proved in a stronger stability version. 相似文献
17.
A polynomial, called the Penrose polynomial, is studied for binary matroids, generalizing previous work on plane graphs. In particular, several formulae of Penrose are extended via the theory of isotropic systems. (Received 9 February, 2000; in revised form 26 June 2000) 相似文献
18.
We explore the geometry of isothermic meshes, conical meshes, and asymptotic meshes around the Christoffel dual construction
of a discrete minimal surface. We present a discrete Legendre transform which realizes discrete minimal surfaces as conical
meshes. Conical meshes turn out to be infinitesimally flexible if and only if their spherical image is isothermic, which implies
that discrete minimal surfaces constructed in this way are infinitesimally flexible, and therefore possess reciprocal-parallel
meshes. These are discrete minimal surfaces in their own right. In our study of relative kinematics of infinitesimally flexible
meshes, we encounter characterizations of flexibility and isothermicity which are of incidence-geometric nature and are related
to the classical Desargues configuration. The Lelieuvre formula for asymptotic meshes leads to another characterization of
isothermic meshes in the sphere which is based on triangle areas.
Authors’ addresses: Johannes Wallner (corresponding author), Institut für Geometrie, TU Graz, Kopernikusgasse 24, A 8010 Graz,
Austria; Helmut Pottmann, Institut für Diskrete Mathematik und Geometrie, TU Wien, Wiedner Hauptstr. 8-10/104, A 1040 Wien,
Austria 相似文献
19.
E.G. Coffman Jr. George S. Lueker Joel Spencer Peter M. Winkler 《Probability Theory and Related Fields》2001,120(4):585-599
A random rectangle is the product of two independent random intervals, each being the interval between two random points
drawn independently and uniformly from [0,1]. We prove that te number C
n
of items in a maximum cardinality disjoint subset of n random rectangles satisfies
where K is an absolute constant. Although tight bounds for the problem generalized to d > 2 dimensions remain an open problem, we are able to show that, for some absolute constat K,
Finally, for a certain distribution of random cubes we show that for some absolute constant K, the number Q
n
of items in a maximum cardinality disjoint subset of the cubes satisies
Received: 1 September 1999 / Revised version: 3 November 2000 / Published online: 14 June 2001 相似文献